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Marianna [84]
3 years ago
8

Fill in the blanks below to make a true statement. In a binomial experiment with n trials and probability of success p, if np (1

- p) ≥ 10, the binomial random variable X is approximately normal with mu X= ___ and sigma X= _____
a. 10. 100.
b. np ( 1 - p ) . 5. np.
c. np/( 1 - p ).
Mathematics
1 answer:
Sergeu [11.5K]3 years ago
3 0

Answer:

\mu_{x}=np

\sigma^2_{X}=np(1-p)

Step-by-step explanation:

∵ When x is a random variable having distribution B(n, p), then for sufficiently large value of n, the following random variable has a standard normal distribution,

\frac{x-\mu}{\sigma}\sim N(0,1)

Where,

\mu=np

\sigma^2=np(1-p)

Here the variable X has a binomial distribution,

Such that, np (1 - p) ≥ 10 ⇒ n is sufficiently large.

Where, n is the total numbers of trials, p is success in each trials,

So, the mean of variable X is,

\mu_{X} = np

And, variance of variable X is,

\sigma^2{X}=np(1-p)

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